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Model Reduction Methods in Option Pricing

Author

Listed:
  • Francisco Chinesta

    (LMSP - Laboratoire de Mécanique des Systèmes et des Procédés - CNRS - Centre National de la Recherche Scientifique)

  • Antonio Falcó
  • Mariano González

Abstract

In this work we introduce the Proper Orthogonal Decomposition (POD) approach to the valuation of contingent claims for one–dimensional price models. First, we present the POD in the context of an abstract Hilbert space and we give an application for the numerical pricing of Double Barrier Options. In a finite dimension setting, we show the model reduction method for Finite Difference schemes of implicit type. In particular, we construct the reduced version of the Crank–Nicolson scheme and some numerical examples are given.

Suggested Citation

  • Francisco Chinesta & Antonio Falcó & Mariano González, 2006. "Model Reduction Methods in Option Pricing," Post-Print hal-00289700, HAL.
    • Handle: RePEc:hal:journl:hal-00289700
    Note: View the original document on HAL open archive server: https://hal.science/hal-00289700
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    References listed on IDEAS

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    1. Dmitry Davydov & Vadim Linetsky, 2003. "Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach," Operations Research, INFORMS, vol. 51(2), pages 185-209, April.
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    More about this item

    Keywords

    Model Reduction; Proper Orthogonal Decomposition; Finite Difference Schemes; Crank-Nicolson Scheme;
    All these keywords.

    JEL classification:

    • G34 - Financial Economics - - Corporate Finance and Governance - - - Mergers; Acquisitions; Restructuring; Corporate Governance
    • M14 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Corporate Culture; Diversity; Social Responsibility
    • M42 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Auditing

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